This paper presents detailed studies on the bistability exhibited by the Langmuir-wave driven by a two-frequency laser. The equations governing the evolution of the amplitude and phase of the Langmuir-wave are derived fully relativistically. The bistable responses of both the saturated amplitude and steady amplitude of the Langmuirwave with respect to plasma frequency and pump intensity are studied, and the applications of hysteresis to laser-plasma Beat-Wave Accelerator are discussed. Finally the properties of the time evolution of the Langmuir-wave amplitude near the critical poim of the bistability are also investigated.
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